What methods can be used to cut irregular shaped holes in flat beveled surfaces with clean topology?
I don't know if this will help you (maybe post your blend file?) but I recently learned about the Offset Edges plugin (needs to be downloaded and installed from file).  This works something like the way I would expect the "Shrink/Fatten" tool to work with a loop of edges--it will extrude them (or duplicate them, or move them) inwards or outwards in a way that does not distort the outline of the loop.

https://wiki.blender.org/index.php/Extensions:2.6/Py/Scripts/Modeling/offset_edges

How you might use that here, in a sample file that is maybe a little like your example.


The face to be created is between the top edge of the cylinder and the surrounding square edge.





Since these are two separate edge loops, we will offset each of them separately.  First the square edge, using Mesh-->Edges-->Offset Edges-->Extrude





Then offset the circle loop using the same command:





Now we can fill our remaining face, either using Mesh-->Faces-->Fill or Mesh-->Edges-->Bridge Edge Loops:





Et voila, the ugly triangle topology of the filled flat face does not impact the edges (in this case) because it is "buffered" by a margin of proper topology.




How this may work out in your case is hard to say for certain, but it's worth a try.